General Relativistic Collapse of an Axially Symmetric Star. I: The Formulation and the Initial Value Equations

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Abstract
Using the ADM formalism, we give a method of solving the general relativistic collapse of an axially symmetric star by the numerical calculation. At t=0, we solve the constraint equations to determine the initial data of the metric tensors and the extrinsic curvatures under given angular momentum distribution and baryon number distribution. An example of the initial data is shown. At later time the evolution equations of the metric and the hydrodynamics equations are solved. The constraint equations are not solved but used to see the accuracy of the numerical calculation. The details of the numerical techniques are shown for the spherically symmetric case.

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